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PS1000 Sec1 Q10

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by joyseychow » Wed Feb 11, 2009 4:51 am
Is there a faster way of calculating this other than listing it by rows? Maybe a formula?

What is the total number of integers between 100 and 200 that are divisible
by 3?
(A) 33
(B) 32
(C) 31
(D) 30
(E) 29
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by mals24 » Wed Feb 11, 2009 5:10 am
Well you can calculate this in 2 ways:

1: 100-200

The First Number divisible by 3 in this range is 102 and the last is 198

(A number is divisible by 3 if the sum of the digits is a multiple of 3)

102/3 = 34
198/3 = 66

So number of digits between 34-66 (inclusive) = (66-34) + 1 = 33

2: 200/3 = 66.67
So from 1-200 there are 66.67 numbers that are divisible by 3

100/3 = 33.33
So from 1-100 there are 33.33 numbers that are divisible by 3

Hence 100-200 = 66.67-33.33 = 33 approx
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by ellexay » Wed Feb 11, 2009 5:44 pm
I don't know if this is just coincidence, but I actually got the answer this way -

198/3 = 66 (i chose 198 because it's the first number counting down from 200 that's divisible by 3)

66/2 = 33 (i figure that half of those 66 numbers will be divisible by 3).

Can someone verify whether this is a coincidence?
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Re: PS1000 Sec1 Q10

by x2suresh » Wed Feb 11, 2009 8:56 pm
joyseychow wrote:Is there a faster way of calculating this other than listing it by rows? Maybe a formula?

What is the total number of integers between 100 and 200 that are divisible
by 3?
(A) 33
(B) 32
(C) 31
(D) 30
(E) 29
smallest integers that is divisiable by 3 in the range 100 and 200
= 3
largest integer that is divisble by 3 in the range 100 and 200
= 198

Anser = (198-3)/3 +1(to include 3 smallest integer) = 65+1 =66.
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by billzhao » Wed Feb 11, 2009 9:16 pm
Using methods of sequence.

A1=102, An=198 and d=3

now we need to find n:

knowing that: An=A1+(n-1)*d

we have: 198=102+(n-1)*3, we can get that n=33

Answer is (A)
Yiliang
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Re: PS1000 Sec1 Q10

by x2suresh » Wed Feb 11, 2009 9:50 pm
x2suresh wrote:
joyseychow wrote:Is there a faster way of calculating this other than listing it by rows? Maybe a formula?

What is the total number of integers between 100 and 200 that are divisible
by 3?
(A) 33
(B) 32
(C) 31
(D) 30
(E) 29
smallest integers that is divisiable by 3 in the range 100 and 200
= 102
largest integer that is divisble by 3 in the range 100 and 200
= 198

Anser = (198-102)/3 +1(to include 3 smallest integer) = 32+1 =33.
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